Chapter 24, Problem 17A

What is the ideal efficiency of a heat engine that operates with its hot reservoir at 500 K and its sink at 300 K?

To determine

To Calculate:Ideal efficiency of a heat engine.

Answer to Problem 17A

  $40\%$

Explanation of Solution

Given:

Temperature of cold reservoir, $T_{low}=300\text{K}$

Temperature of hot reservoir, $T_{high}=500\text{K}$

Formula used:

Ideal efficiency:

  $\eta =1-\frac{T_{low}}{T_{high}}$

Calculation:

Substitute the values and solve:

  $\begin{array}{c}\eta =1-\frac{T_{low}}{T_{high}}\\ =1-\frac{300}{500}\\ =0.4=40\%\end{array}$

Conclusion:

The ideal efficiency of the heat engine is $40\%$ .